14th Putnam 1954

Show that for any positive integer r, we can find integers m, n such that m² - n² = r³.

Solution

Easy.

We notice that m² - n² = (m + n)(m - n). This suggests taking m + n = r², m - n = r. This works: m = r(r + 1)/2, n = r(r - 1)/2.

14th Putnam 1954

© John Scholes
jscholes@kalva.demon.co.uk
24 Nov 1999